Which of the following statements is false?

Body compensates for low oxygen availability at high altitudes by:
$I.$ Increasing $RBC$ production
$II.$ Decreasing the binding affinity of haemoglobin
$III.$ Increasing the binding affinity of haemoglobin
$IV.$ Increasing the breathing rate
$V.$ Decreasing the breathing rate
Choose the correct option for the given statement.

Select the correct option:
$(1)$ The respiratory rhythm center for breathing regulation is located in the medulla oblongata of the brain.
$(2)$ Each hemoglobin molecule can carry a maximum of $4$ molecules of $O_2$. (Note: The original question mentioned $CO_2$,which is incorrect; hemoglobin primarily transports $O_2$.)

What is the approximate amount of $CO_2$ eliminated by our lungs per day?

Which of the following is a respiratory gas?

Which of the following is functional for protection against the environmental abiotic factor of temperature or for thermoregulation of the living body during winter or summer?